## Related questions with answers

Credit Card Debt John has a balance of $3000 on his Discover card that charges 1% interest per month on any unpaid balance. John can afford to pay$100 toward the balance each month. His balance each month after making a $100 payment is given by the recursively defined sequence$B_{0}=$3000 \quad B_{n}=1.01 B_{n-1}-100$ Determine John's balance after making the first payment. That is, determine $B_{1}$.

Solution

Verified$\text{\color{#4257b2}We need to determine the first payment term\ $(B_{1})$\ for the following expression.}$

$\color{Brown}B_{0}=3000\text{\ Dollars}\ \ \ \ \ \ \ \ \ \ \ \ B_{n}=1.01\ B_{n-1}-100$

$\lozenge$\ $\text{\underline{\bf{Solution:}}}$

To get any term, substitute the number of term in the expression which given as follows:

$B_{n}=1.01\ B_{n-1}-100$

$B_{0}=3000$

$B_{1}=1.01\ B_{1-1}-100\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B_{1}=1.01\ B_{0}-100$

$B_{1}=(1.01\cdot3000)-100\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B_{1}=3030-100$

$B_{1}=2930\ \text{Dollars}$

So, the first payment term is \ $2930$\ dollars

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